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Results tagged with knots
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user 50
Questions about exploring knot theory using Mathematica.
8
votes
RegionPlot3D KnotData
You can feed the BoundaryMeshRegion[] you can obtain from KnotData[] into RegionPlot3D[]. For example:
trefBMR = KnotData["Trefoil", "BoundaryMeshRegion"];
RegionPlot3D[RegionMember[trefBMR, {x, y, z} …
4
votes
Issue Plotting Torus Link
The (1,4) torus knot is known to KnotData[], so we can use that to build the (2,8) knot:
knot14 = First[KnotData[{"TorusKnot", {1, 4}}, "ImageData"]];
Graphics3D[MapThread[Insert[##, {2, 1}] &,
…
3
votes
Intersection between knot and plane
For completeness, here is how to use the MeshFunctions approach in the general case of a plane defined by three noncollinear points:
sc = KnotData["FigureEight", "SpaceCurve"];
threepoints = N[{{0, 0 …